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\sqrt{3}-\frac{\sqrt{1}}{\sqrt{3}}
Rewrite the square root of the division \sqrt{\frac{1}{3}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3}}.
\sqrt{3}-\frac{1}{\sqrt{3}}
Calculate the square root of 1 and get 1.
\sqrt{3}-\frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}
Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.
\sqrt{3}-\frac{\sqrt{3}}{3}
The square of \sqrt{3} is 3.
\frac{3\sqrt{3}}{3}-\frac{\sqrt{3}}{3}
To add or subtract expressions, expand them to make their denominators the same. Multiply \sqrt{3} times \frac{3}{3}.
\frac{3\sqrt{3}-\sqrt{3}}{3}
Since \frac{3\sqrt{3}}{3} and \frac{\sqrt{3}}{3} have the same denominator, subtract them by subtracting their numerators.
\frac{2\sqrt{3}}{3}
Do the calculations in 3\sqrt{3}-\sqrt{3}.